There are known winding machines for the production of wound rolls from paper or cardboard webs, subdivided by longitudinal cutting into individual webs, wherein winding stations are arranged on both sides of a central support roller, each winding station consisting of two support elements, the individual webs being alternately supplied to them for winding. Each winding station holds a windup roll by means of guide heads rotatably supported on the support elements, which engage laterally into the respective windup tube. Thereby the guide heads bear the entire or partial weight of the roll, in order to keep line force at the contact line with the support roller, which is decisive for the winding quality, within a desired low range.